Adaptive Penalty and Barrier function based on Fuzzy Logic

Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance.

Comparison Among Aerobic Exercise and Other Types of Interventions to Treat Depression: A Systematic Review

Depression is a common and disabling disease that affects over 100 million people worldwide and can have a significant impact on physical and mental health, reducing their quality of life. Thus, the aim of this article was to provide information on research results and key chains related to the therapeutic effects of chronic aerobic exercise compared with other types of interventions to treat depression, which may become a useful clinical application in a near future. Researches have shown the effectiveness of alternative treatments, such as physical exercise, minimizing high financial costs and minimizing side effects. In this review, the data analyzed allows us to claim that alternative therapies, such as exercise, are effective on controlling and reducing symptoms. 69.3% of the studies that investigated the antidepressant effects of exercise on depressive were significant, and the other 30.7% of the studies improved only in general physiological aspects, such as increased oxygen uptake, increased use of blood glucose and decreased body fat percentage, with no improvement on symptoms of depression. From the sample analyzed, 71.4% was composed of women, and regarding the severity of symptoms, 85% had mild to moderate depression and only 15% had moderate to severe depression. However, there is still disagreement regarding the effect of exercise compared to the use of antidepressants in symptomatology and cognitive function in depression, this suggests that there is no consensus on the correct intensity of aerobic exercise as to achieve the best dose-response, with intensities high to moderate or moderate to mild.